Block #846,793

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/9/2014, 9:08:42 PM · Difficulty 10.9721 · 5,998,335 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

426e1f25f8283355d7eee4ba44c1fcb682f93cf17b941702de0a0ee5fd370f92

View on Chainz ↗

Height

#846,793

Difficulty

10.972130

Transactions

Size

650 B

Version

Bits

0af8dd88

Nonce

800,859,522

Timestamp

12/9/2014, 9:08:42 PM

Confirmations

5,998,335

Mined by

⛏️ P2SHAULY2pjcxaZL8LG72BvVyaaH2AephkB2qi

Merkle Root

311d68225a2f9bc0dd33b4d7bbc0ef69a6da1c73f6d581b5a9fea6b052cb1985

Transactions (3)

Coinbase33300fefdca44e…d0625f00b40101

1 in → 1 out8.3200 XPM109 B

AULY2pjc…ephkB2qi

bdd57b76a684a5…41234183120c96

1 in → 2 out0.1335 XPM225 B

AWwws15E…hFKMjb2p AUXc2J2R…WALTRDzZ

bd33b593960108…4a1638cfc14662

1 in → 2 out0.0914 XPM225 B

AHpQRMUe…iVoYm1Co ASn353KN…C5Vv1sti

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.383 × 10⁹⁶(97-digit number)

33832768542742756591…85717036761174138879

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

3.383 × 10⁹⁶(97-digit number)

33832768542742756591…85717036761174138879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.383 × 10⁹⁶(97-digit number)

33832768542742756591…85717036761174138881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

6.766 × 10⁹⁶(97-digit number)

67665537085485513183…71434073522348277759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.766 × 10⁹⁶(97-digit number)

67665537085485513183…71434073522348277761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.353 × 10⁹⁷(98-digit number)

13533107417097102636…42868147044696555519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.353 × 10⁹⁷(98-digit number)

13533107417097102636…42868147044696555521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.706 × 10⁹⁷(98-digit number)

27066214834194205273…85736294089393111039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.706 × 10⁹⁷(98-digit number)

27066214834194205273…85736294089393111041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.413 × 10⁹⁷(98-digit number)

54132429668388410546…71472588178786222079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.413 × 10⁹⁷(98-digit number)

54132429668388410546…71472588178786222081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.082 × 10⁹⁸(99-digit number)

10826485933677682109…42945176357572444159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #846,793

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